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Find the measure of each angle of the quadrilateral.​

Find the measure of each angle of the quadrilateral.​-example-1

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all work should be in the picture, lmk if theres anything confusing

Find the measure of each angle of the quadrilateral.​-example-1
User Triamus
by
8.6k points
6 votes

Answer:

  • ∠D = 45°
  • ∠E = 95°
  • ∠F = 85°
  • ∠G = 135°

Explanation:

You want the measures of each angle in the quadrilateral marked D = (2x+18)°, E = (8x -13)°, F = (6x+4)°, G = 10x°.

Sum of angles

The sum of angles in a quadrilateral is 360°, so we have ...

D +E +F +G = 360°

(2x+18)° +(8x-13)° +(6x+4)° +10x° = 360°

26x +9 = 360 . . . . . . . . . divide by °, collect terms

26x = 351 . . . . . . . . . subtract 9

x = 13.5 . . . . . . . . divide by 26

Angle measures

The angle measures are found by using this value of x in the expression for each:

D = (2(13.5) +18)° = 45°

E = (8(13.5) -13)° = 95°

F = (6(13.5) +4)° = 85°

G = 10(13.5)° = 135°

__

Additional comment

We note that left-side angles total 180°, as do right-side angles. This means DE║FG and the figure is a trapezoid.

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Find the measure of each angle of the quadrilateral.​-example-1
User Mrowe
by
8.2k points

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